Abstract

Verified Computation of Bounds for Special Functions by Use of Generating Function R. Lohner Methods for the computation of safe bounds for the values of special functions are not yet developed very far. We demonstrate that if a generating function is available for such functions (which is the case for Bessel functions and for many orthogonal polynomials) then with the tools of interval arithmetic and automatic differentiation such bounds can be obtained in a very easy way. If the generating function is singular at the origin then bounds can still be computed by sampling this generating function on a small circle around the origin and applying an interval fast Fourier transformation.

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